As done in the appendix of [1]}, we separate the \(l=0\)  and the \(l=2\)  cases. Looking first at the more complicated case of \(l=0\) , we must ensure that \(\left|\xi _{\alpha \beta }\right\rangle \)  is orthogonal to the considered ground–state [(in our case, the ansatz of Eq. (REF )]. As such, to ensure this, we must have
\(\left\langle \psi _{0}|\xi _{\alpha \beta }\right\rangle & = \sum _{n=1}^{+\infty }\zeta _{0,n}^{\alpha ,\beta }\left(\omega _{a},\omega _{b}\right)\left\langle \psi _{0}|J_{0}\left(z_{0,n}\frac{r}{R}\right)\right\rangle \nonumber \\& = 0,\) 
